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Computational Astrophysics

Logistics and Overview

Course Overview
Using These Notes

Tour of Python

Jupyter
Python Basics
Functions and Classes
- Functions
- Classes
NumPy
matplotlib

Git and Github

Version Control
A Git Walkthrough
Git Branches
Git Remotes
github
Pull requests

Fundamentals

Floating Point Format
- Numerical Errors: Roundoff and Truncation
Differentiation
Integration
Root finding
Linear Algebra

Ordinary Differential Equations

Basic Methods for ODEs
- 2nd Order Runge-Kutta / Midpoint Method
- 4th-order Runge-Kutta
Adaptive Timesteps
In-Class Example
ODEs and Conservation
- Time Symmetric Integration
Two Point Boundary Value Problems
- Application: Stellar Structure
More Applications

Working with Data Samples

Fourier Transforms
Interpolation
Least Squares Regression

Partial Differential Equations

Partial Differential Equations
Advection
Burgers’ Equation
- Burgers’ Riemann Problem
- Solving Burgers’ equation
Poisson problem
Multigrid
Diffusion

Hydrodynamics

Euler Equations
Euler equations eigensystem
Euler Riemann problem
Sampling the Riemann solution
Second-order Euler solver

Stiff ODEs

Implicit Methods for ODEs
Implicit Methods for Systems of ODEs
Implicit Methods and Nonlinear Systems
Application: Nuclear Reaction Networks
- Integration Example

Magnetohydrodynamics

Magnetohydrodynamics Equations
Solving the Riemann problem in MHD

Machine Learning

Artificial Neural Network Basics
Hidden Layers
Diving Deeper into Machine Learning
Machine Learning in Astronomy

Homework

Homework 1
Homework 2
Homework 3
Homework 4

Repository
Open issue

Index

By Michael Zingale

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